practice-2401-2

practice-2401-2 - x 2 + y = 1 and z 2 + y = 1 : Problem 6:...

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Practice Exam II, Calculus III (Math 2401) 1
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2 Problem 1: Use di/erential to estimate the change in T = x 2 cos y 2 sin from x = 2 ; y = 2 ; z = 2 to x = 2 : 1 ; y = 1 : 9 ; z = 2 : 2 : Problem 2: Determine whether not the vector function 2 ln (3 y ) + 1 x ± i + 2 x y + y 2 ± j Problem 3: (a) Evaluate the double integral R R e y 2 = 2 dxdy , where is the trian- gular region bounded by the y axis, 2 y = x and y = 1 : (b) Calculate the average of f ( x; y ) = xy over the region ± x ± 1 ; 0 ± y ± p 1 x 2 : Problem 4: Find the volume of the solid bounded above by the surface z = 1 x 2 y 2 ; below by the xy plane, and on the sides by the cylinder x 2 + y 2 x = 0 . Problem 5: Evaluate the triple integral R R R T y 2 dxdydz; where T is the
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Unformatted text preview: x 2 + y = 1 and z 2 + y = 1 : Problem 6: Find the volume of the solid bounded above by the sphere x 2 + y 2 + z 2 = 4 and below by the plane z = 1 : 3 Answers : 1. T decreases by about 4 5 & & 2 5 = 2 : 11 : 2. The gradient of f ( x; y ) = 2 x ln (3 y ) + ln j x j + y 3 3 + C: 3. (a) 2 & 1 & 1 p e : (b) The area of & = 1 4 & (quarter disk of radius 1 ). The average value is 1 2 & . 4. V = R & 2 & & 2 R cos 1 & r 2 r drd = 5 & 32 : 5. R 1 R 1 & x 2 R p 1 & y y 2 dzdydx = 1 12 : 6. 5 &= 3 :...
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practice-2401-2 - x 2 + y = 1 and z 2 + y = 1 : Problem 6:...

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